If Bitcoin becomes large enough it is only a matter of time before a bank offers the ability to exchange Bitcoins for fiat currency and offers depository services.
In contrast to franky1's dogmatic statements, I agree with you here. Banks getting involved with Bitcoin will probably happen, and will probably get more of the masses involved in Bitcoin.
The danger we need to convey to these masses is that, once banks start holding Bitcoin deposits, their previous experience with fiat will motivate them to loan out more than they hold (i.e. fractional reserves). Somehow, the community needs to get ahead of this and get the message out that a bitcoin-IOU is NOT the same as a bitcoin. Or, as Holliday so aptly puts it: "If you aren't the sole controller of your private keys, you don't have any bitcoins."